Day 1 - Reviewing Exponential Functions
Wednesday November 16, 2010
Edited by: Mariam

Form of the Function: f(x) = b ^ x b- base x - exponent (variable)

	f(x) = 2^x	f(x) = (1/2)^x
Domain	{x| xER}	{x|xER}
Range	{y|y>0, yER}	{y|y>0, yER}
y-intercept	1	1
any asymptotes? where?	y = 0	y= 0

What are the finite differences of y = 2^x

x	y	∆y1	∆y2	∆y3	∆ Y4
0	1	1	1	1	1
1	2	2	2	2	2
2	4	4	4	4	4
3	8	8	8	8	8
4	16	16	16	16
5	32	32	32
6	64	64
7	128

Therefore, can conclude that the finite differences of the exponential functions are exponential as well, and copy the actual functions values.

Working with Exponential Expressions and Equations - Examples

1. 1. 2^x = 4 2^x = 2^2 x = 2	2. 2^x = 16 2^x = 2^4 x= 4
3. 4^ (x+5) = 64^x 4^ (x+5) = 4^(3x) x+5 = 3x 5 = 2x 5/2 =x	4. 4^ (2x) = 8^ (x-3) 2^ (4x) = [2^3]^(x-3) 2^ (4x) = 2^(3x – 9) 4x = 3x-9 x= -9

Homework: Exponential Expression and Equations multiple choice hand out

For more information visit:
Grade 11 Exponential Functions Review
Exponent Laws (check out if you had difficulty with the homework)

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Day 2- Logarithms

By: Gwynne Finlay

Sorry, I don't know how to make the font subscript. So, I just wrote subscript after the number. Mostly the numbers are after the log so just to let you know that means it has to be "the little writing".

--> y=b^x is an example of an exponential function.

--> the logarithm is the inverse of the exponential function

inversegraph.gif

b --> base

x=b^y
logbx=y (said "log base b of x is equal to y")

eg. express as a logarithm
a) 2^4=16
--> log2(subscript)16=4

b) a^c=d
--> loga(subscript)d=c

eg. express as an exponent
a)log5(subscript)125=3
--> ^3=125

b) loge(subscript)f=k
-->e^k=f

eg. solve
a) log3(subscript)81
3^x=81
3^x=3^4
x=4

Common Logarithm

--> the log button on your calculator is to the base of 10 --> log10(subscript)
you can only use the log button on your calculator if the subscript after is a 10
eg.
a) log10(subscript)100
x=2

b) log 10000 <-- when nothing is placed after the log it means that there is an invisible 10 there.
x=4

c) log120
x=2.08

Homework: -- to finish the "Home Activity" worksheet
Wise Words from Gillian -- make sure to understand exponential functions so that you can understand logarithms!
-- make sure to do the previous sheet (solving exponential functions) and understand it because you use them often!

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Monday November 22 2010
Brittney West
I have posted this morning's lesson below.

Gillian gave us a homework sheet today in class. Also, we are to derive the quotient rule. (see lesson)
Remember to check your email tonight about tomorrows field trip!

If you're struggling with this topic, here's a helpful link:
http://www.purplemath.com/modules/logrules.htm

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Path System

Tuesday, November 23
Mimi Chen

Today we had a field trip to downtown Toronto where we did math in public places! We learned that math can be found anywhere, and that people stare when you walk with a calculator in hand.

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Monday November 29 2010
Brittney West
Tomorrow we have a quiz!! Below I have posted an attachment to a brief summary as well as today's lesson. Gillian handed out our "Bonus Assignment" today which is due on Friday!


If you're struggling with any of these topics, the website below is very helpful! :)
http://www.purplemath.com/modules/logrules.htm

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Topic: Applications of Logarithms
Tuesday November 30th, 2010
Edited by: Mariam Naguib

Today we had a LOG quiz, a Teamwork Tuesday (handed in, in class) and a short lesson (attatched below)


Homework: Applications Hand Out + Textbook pg. 131 # 1-12, pg. 134 # 1-19, pg. 148 #2, 6, 10, 11.
For more info: Richter Scale and pH Scale
Sample Word Problems

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Wednesday, December 1, 2010
Edited by Robert Piggott

MATH AT MAC - math contest today!!!!

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Friday, December 3rd, 2010 - Transforming Log Functions
Edited by: Aleena Dipede

To begin, we got in partners and discussed the following questions and these are some of the idea we came up with.

Question 1: A negative integer is the logarithm (base 10) of the number A. What do you know about number A?
- it's an exponent of 10
- 0 < a < 1
- A is always postive

Question 2: A number in the form _.5 where _ is a whole number, is a logarithm (base 10) of the number A. What do you know about A?
- A ≥ √4
- log4A = _.5
- 4_.5= A

Here is a summary of the activity we did on the GIZMO. If you would like to access the GIZMO the login is TORONDSB1269 and the pass is science.

Here's the gist...

The standard form of the logarithm is y = logb(x)
Where b and x are both positive integers and b ≠1

The x-intercept of the standard function is always 1
The asymptote of the standard function is x=0, so the graph can never touch the y-axis.

Image from: http://www.bymath.com/studyguide/fun/sec/fun9.htm
When a > 1 the graph curves up and when 0 < a < 1 the graph curves downwards.

Now when we transform the function it takes this form

Y = a logb [c(x-h) + k]

"h" is a phase shift and moves the asymptote and changes the restrictions in the domain.
Example. Horizontal Shifts


Image from: http://www.pindling.org/Math/CA/By_Examples/4_3_Logarithm/4_3_logarithms.html

"k" is a verticle translation
Example. Vertical Shifts


Image from: http://www.pindling.org/Math/CA/By_Examples/4_3_Logarithm/4_3_logarithms.html
"a" is a verticle stretch or compression and if (-ve) a reflection in the x-axis

"c" is a horizontal stretch or compression

Our homework is to start studying by finishing up any homework that has not been completed yet (including the lesson on the GIZMO and the review package we recieved)


If you want more information this link has three pages on transforming logs and goes through examples, pretty helpful... http://www.purplemath.com/modules/graphlog.htm

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Tuesday December 7 2010
By: Sarah Drury
Today we wrote our Exp/Trig unit test.

December 10
Gwynne Finlay
Today we worked on the computer.